Sen. Rand Paul (R-Ky.) said Thursday he intends to "explore" a run for president in 2012 should his father, Rep. Ron Paul (R-Texas), decide against another campaign. 

"He has not made his mind up," Paul said of his father at a Thursday appearance in Kentucky. "If he does not run, I have not ruled it out, and I will think about it." 

Earlier in the day, Paul told a Kentucky radio station that if the Texas congressman doesn't run, "then I think there are options open and we will explore those options."

After Thursday's event, Paul also told the AP that supporters in a number of states are encouraging him to pursue the presidency in 2012 should his father opt out.  

At an appearance earlier this week in South Carolina, the first-term senator and member of the Senate's Tea Party Caucus said the only decision he's made on 2012 is that he won't run if his father opts for a bid. 

The elder Paul is seriously considering what would be his third presidential bid, but hasn't made an official decision. 

Rand Paul has trips to both Iowa and New Hampshire on his schedule in the coming weeks.